The mass of the Martian satellite Phobos has been determined by processing radiometric tracking data obtained from the Viking-1 spacecraft during a series of 14 near encounters which occurred in February 1977. Distances of closest approach ranged from 89 to 213 km from the center of mass of the satellite. Our best estimate for the gravitational constant, GM, of Phobos is (6.6¿0.8) ¿10-4 km3/s2. The corresponding density of Phobos based on a volume estimate of 4800¿960 km3 from Mariner 9 imaging is 2.0¿0.5 gm/cm3.